摘要
对多维走时反演提出一种可实现的递推算法,并对研究动机和应用背景及主要技术路线进行简要阐述.本文的递推算法是非迭代型的.根据成象区边界相对于积分沉形的凸的性质,或等价地根据非线性走时方程组中的三角结构,可以由外及里地逐层反演成象区内的慢度.本文的方法具有节省计算时间、占内存少和直观的特点.
A non-iteration algorithm for solving multidimensional non-linear travel-time inversion is proposed. Because the ray paths depend on the velocity of the medium, it is a nonlinear problem to invert the velocity in a region from the travel-time data measured on its boundary. We illustrate the algorithm in terms of seismic longitudinal wave travel-time inversion. In the algorithm it is assumed that the angular coverage of the ray is complete, the image region has limited boundary, the velocity outside the image region is known. The travel-time between two arbitrary points on the boundary is given. It is also assumed that the velocity in the image region can be expressed as a linear combination of local base functions. In the first step, the velocities in the pixels adjacent to the boundary are inverted. Based on the fact that there must be a ray travelling through the only one pixel adjacent to the boundary, the data of this ray can be used to invert the velocity of the pixel which lead to solve an nonlinear equation with one unknown. In this way, the velocity of all the pixel closed to the boundary can be worked out. After that, we trace all of other rays from two terminals of the ray to the new boundary of unknown region and give two new terminals and travel-time of ray travelling through reduced unknown region. The ray directions at every two terminals in the first step can be determined by differentiating the travel-time of the neighbour ray from the Benndorf relation. Then the ray tracing is a initial value problem and can be calculated easily. The ray direction at two new terminals and traveling-time can be given in the ray tracing. Then the problem left is all the same as last step, but the unknown region is reduced and the algorithm used in the first step is repeated. In this way, the velocity of image region is inverted from outer layer to inner layer by layer stripping until the velocity of all the region is worked out.From the algorithm above, it can be seen that the inversion procedure can be finished in
出处
《地球物理学进展》
CSCD
1992年第4期29-37,共9页
Progress in Geophysics
基金
国家基金委
石油天然气总公司资助
大庆石油天然气管理局资助
中国科学院联合资助课题
关键词
多维走时反演
非线性
递推法
Multidimensional ray travel-time mversion
Nonlinear
Layer stripping
